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Extremal solutions of second order nonlinear periodic boundary value problems. (English) Zbl 0723.65056
The authors consider the periodic boundary value problems of the form $- u''(t)=f(t,u(t),u'(t)),\text{ for } a.e.\quad t\in [0,2\pi],\quad u(0)=u(2\pi),$ where f is a Carathéodory function. They develop a monotone method to obtain the existence of extremal solutions between the lower and upper solutions as uniform limit of monotone sequences. This result is a generalization of results earlier obtained by the second author to the case of functions f depending also on $u'$.
Reviewer: H.Weber (Wiesbaden)

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
Full Text: DOI
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[5] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathéodory functions, Applicable Anal., to appear.
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[7] Vainberg, M.: Variational methods for the study of nonlinear operators. (1964)